Time, space, and episodicity of physical disturbance in...

Time, space, and episodicity of physical disturbance in streams

Daniel Millera,*, Charlie Luceb, Lee Bendac

aEarth Systems Institute, WA 3040 NW 57th Street, Seattle, WA 98107, USAbBoise Aquatic Sciences Lab, Rocky Mountain Research Station 316 E. Myrtle, Boise, ID 83702, USA

cEarth Systems Institute, CA 310 N Mt. Shasta Blvd., Suite 6, Mt. Shasta, CA 96067, USA

Abstract

Storm-driven episodes of gully erosion and landsliding produce large influxes of sediment to stream channels that have both

immediate, often detrimental, impacts on aquatic communities and long-term consequences that are essential in the creation and

maintenance of certain channel and riparian landforms. Together, these effects form an important component of river

ecosystems. In this paper, we describe issues involved in characterizing and predicting the frequency, magnitude, spatial

extent, and synchrony of these sediment influxes. The processes that drive sediment fluxes exhibit spatial and temporal

variability over a large range of scales. Disregard of this variability can have unanticipated consequences for efforts to quantify

process rates, as we illustrate using landslide densities observed for a storm event in western Oregon. Multiple factors interact to

create the temporal and spatial patterns of erosional and mass-wasting events that affect stream channels. Fires, in particular,

enhance susceptibility to erosional and mass-wasting processes, and thus affect the timing and magnitude of sediment-

mobilizing events. We use examples from west-central Idaho to show how fires, storms, and topography interact to create

spatially distinct patches of intense erosional activity. We require quantitative descriptions of these controlling factors to make

quantitative predictions of how differences or changes in topography, fire regime, and climate will affect the regime of sediment

fluxes. The stochastic and heterogeneous nature of these factors leads us to quantify them in probabilistic terms. The effects of

future fire and storm sequences are governed in part by the past sequence of events over time frames spanning centuries and

spatial extents spanning entire river basins. Empirical characterization of past events poses a considerable challenge, given that

our observational record typically spans several decades at most. Numerical models that simulate multiple event sequences

provide an alternative means for estimating the influence of antecedent conditions and for quantifying the role of different

controlling factors.

# 2003 Elsevier Science B.V. All rights reserved.

Keywords: Aquatic habitat; Fire; Landslides; Erosion

1. Introduction

Intense or extended rainfall can trigger surface

erosion and landsliding (Caine, 1980) that bring large

and sudden pulses of sediment and organic debris to

stream channels. These events can substantially

impact channel and riparian habitats. Landslides, deb-

ris flows, and consequent debris torrents can scour

channels to bedrock and destroy riparian vegetation

(Hack and Goodlett, 1960; Benda, 1990; Nolan and

Marron, 1990; Cenderelli and Kite, 1998; May, 1998);

local deposition from landslides and debris flows can

bury or block channels (Nolan and Marron, 1988),

create log jams (Hogan et al., 1998), and potentially

Forest Ecology and Management 178 (2003) 121–140

* Corresponding author. Tel.: þ1-206-633-1792;

fax: þ1-425-671-0094.

E-mail address: [email protected] (D. Miller).

0378-1127/03/$ – see front matter # 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0378-1127(03)00057-4

create conditions conducive to dam-break floods

(Coho and Burges, 1993); sediment introduced by

mass wasting and extensive gully erosion can alter

channel characteristics both locally and over many

kilometers, with effects that include channel widen-

ing, reductions in pool frequency, fining of bed

texture, and increased turbidity (Coates and Collins,

1984; Everest et al., 1987; Nolan and Marron, 1990;

Harvey, 1991; Madej and Ozaki, 1996; Montgomery

and Buffington, 1998).

Although these impacts can be detrimental to aqua-

tic communities, the erosional and mass wasting

events that trigger them are also recognized as integral

to the creation and maintenance of certain types of

channel habitat. Landslides and debris flows bring

boulders and large woody debris that provide long-

term sources of channel roughness and complexity

(Everest and Meehan, 1981; Benda, 1990; Grant et al.,

1990; Wohl and Pearthree, 1991; Grant and Swanson,

1995), large, transient increases in sediment supply

create berms, terraces, and fans that shape the valley

floor (Benda, 1990; Madej, 1990; Nakamura et al.,

1995) and create side channels and riparian surfaces

(Miller and Benda, 2000).

The impacts of erosional and mass-wasting events

evolve over time as fluvial transport moves and re-

sorts channel-stored sediment, debris jams decay,

riparian vegetation regrows, and large woody debris

is recruited to channels (Benda, 1990; Nolan and

Marron, 1990; Grant and Swanson, 1995; Hogan

et al., 1998; May, 2001; Pabst and Spies, 2001).

Conditions encountered in channels subject to pulses

of sediment input and transport thus depend on where

in time one intersects this trajectory of change. The

population of sub-basins and tributary channels that

constitute a drainage basin provides many separate

and potentially independent sediment sources. Asyn-

chronous activation of these sources produces a popu-

lation of channel reaches at different points along the

post-event trajectory of channel evolution (Benda

et al., 1998). The past sequence of sediment influx

and transport events thus acts to create and enhance

spatial heterogeneity in channel conditions (Benda

et al., this issue) and contributes to habitat complexity.

Regionally, the mosaic of habitat conditions created

by the sequence and spatial distribution of these events

forms an important component of riverine ecosystem

structure (Reeves et al., 1995).

Fires play an integral role in the timing and severity

of erosional and mass-wasting events (Swanson, 1981;

Meyer et al., 1995; Cannon, 2001; Istanbulluoglu et al.,

2002). Fires can destroy ground cover, reduce soil

infiltration capacity, and kill vegetation, all of which

increase the potential for rainfall-triggered erosion

and mass wasting (Wondzell and King, this issue).

These effects are greatest immediately post-fire and

tend to dissipate over several years, although fire-

related loss of root strength and the associated sus-

ceptibility to landsliding may persist for a decade or

more (Meyer et al., 2001). Thus fires and storms act

together to drive sediment fluxes over a landscape. The

sequence of sediment inflow and transport events

occurring within a river basin arises from the inter-

acting sequence of fires and storms (Benda et al.,

1998). The impacts to stream channels vary over time,

depending on where they are within this sequence.

Other processes, such as disease, windthrow, and snow

avalanches, can also alter vegetation cover and affect

susceptibility to surface erosion and mass wasting, but

fire is the predominant source of vegetation distur-

bance in many landscapes (Agee, 1993).

Storm-driven surface erosion and mass wasting,

accentuated by fire, generate large inputs of sediment

and organic debris to channel systems that are punc-

tuated in space and time (Benda and Dunne, 1997b).

These inputs act to alter the suite of channel and

riparian habitat types and quality found in a basin,

adding to the dynamic and heterogeneous elements of

the river environment. These elements have character-

istic temporal and spatial scales that are governed by

the frequency and magnitude of the sediment inflows,

which in turn are governed by the periodicity, magni-

tude, and timing of fires and storms, modulated by

rates of sediment production (Benda and Dunne,

1997a).

The regime of sediment inflows can be difficult to

characterize, in part because of the extended periods

that may separate large-magnitude events (Kirchner

et al., 2001). Yet, as discussed above, this regime

forms an integral component of a river ecosystem

(Reeves et al., 1995; Gresswell, 1999), and any

changes to that regime pose consequences that are

largely unknown. To anticipate the effects of natural

and anthropogenic change in fire and climate on

stream environments, we must characterize the effects

those changes have on the frequency and magnitude of

122 D. Miller et al. / Forest Ecology and Management 178 (2003) 121–140

sediment influxes and the impact of those influxes on

channels. Benda et al. (this volume) approach the

second topic; here we address the first.

Unfortunately, data to directly quantify the controls

on frequency and magnitude of sediment fluxes are

limited, in large part because of the long periods

involved, so that our understanding of these processes

is largely qualitative and based on inference. Meyer

and Pierce (this volume), show that erosional regimes

have changed over time concurrent with climatic

shifts, but we do not yet have quantitative models

to predict how current and future changes in climate

and fire regime will alter the timing and magnitude of

erosion events. Indeed, it is difficult to quantitatively

characterize current erosion regimes. Erosion and

mass-wasting processes are unevenly distributed in

time and space, which creates a particular challenge

for empirical characterization, as we illustrate using

measures of landslide density in coastal Oregon. Multi-

ple interacting processes drive erosion and mass-wast-

ing events, which complicate attempts to characterize

the factors controlling their occurrence. As an example,

we look at how patterns of stream disturbance depend

on the timing and spatial coincidence of fires and

storms and at how topography and storm characteris-

tics interact to control the spatial distribution of land-

slides in west-central Idaho. Finally, we briefly discuss

methods for quantifying these processes and describe

the use of numerical models for characterizing the

controls on sediment flux.

2. Scale relations and sources of variability

Landslides and debris flows are an important

mechanism for storm-driven pulses of sediment

delivery to channels in many landscapes (Hack and

Goodlett, 1960; Larsen and Simon, 1993; Benda and

Dunne, 1997b; Hovius et al., 1997) and characteriza-

tion of landslide rates is a key component in efforts

to quantify effects of land management on erosion

regimes (Sidle et al., 1985; Montgomery et al., 2000;

Brardinoni, 2001). In February 1996, a high-intensity,

long-duration storm triggered landsliding and flood-

ing across western Oregon. Rainfall intensities and

flood peaks exhibited great spatial variability (Taylor,

1997a); estimated return intervals for flood peaks in

the area spanned a range from less than 10 to over

100 years (Bush et al., 1997). Several studies examined

the effect of forest cover and land management on

landslide densities associated with this storm (Bush

et al., 1997; May, 1998, 2002; Robison et al., 1999).

Although these studies did not include fire-related

landslides, the results are still instructive.

These three studies reported a large range in

observed landslide densities, arising in part from large

spatial variability in storm intensity and from differ-

ences in the study methods. Bush et al. (1997) relied

on landslides identified on 1:24,000-scale aerial

photographs, whereas Robison et al. (1999) and

May (1998, 2002) used field surveys to locate land-

slides and debris flows that reached stream channels.

The study of Bush et al. (1997) encompassed an area

exceeding 4000 km2 including the Siuslaw National

Forest (SNF) and surrounding areas; the Robison et al.

(1999) study involved six sites in western Oregon

following the February storm encompassing an area

of almost 83 km2; May’s survey sites involved 11

third- to fifth-order streams in the Siuslaw Basin with

a combined area of 47 km2. Each survey resulted in

different relationships between relative landslide den-

sity and forest-stand type. All studies found the high-

est average densities in clearcut areas harvested within

the last decade. Results differed substantially, how-

ever, for the relative density of landsliding between

second-growth and older stands. Robison et al. (1999)

consistently found higher densities in stands older than

100 years, whereas May (2002) consistently found

higher densities in second-growth stands (Table 2,

p. 1103). Bush et al. (1997) did not differentiate

between second-growth and older stands. These dif-

ferences illustrate the difficulty in characterizing a

heterogeneous entity and provide an opportunity to

look at how the scale of measurement can affect such

observations.

The Coastal Landscape and Analysis Study

(CLAMS; http://www.fsl.orst.edu/clams/) used data

from Bush et al. (1997) and Robison et al. (1999)

to derive regionally applicable estimates of landslide

susceptibility as functions of forest-cover type for the

Coast Range of Oregon. To examine the effects of

sampling scale, the Bush et al. (1997) inventory

(Fig. 1) was subsampled with replacement (a bootstrap

sample, e.g. Chernick, 1999) at a variety of scales

with landslide densities calculated as a function of

forest type for each sample. Forest type was evaluated

D. Miller et al. / Forest Ecology and Management 178 (2003) 121–140 123

HTTP://WWW.FSL.ORST.EDU/CLAMS/

using the CLAMS vegetation coverage (Ohmann and

Gregory, 2002), with forest classes grouped into three

broad categories: (1) OPEN, consisting of recently

clearcut and unforested land, (2) MIXED, consisting

of forest cover of predominately small conifers or

forests with a predominance of hardwoods, and (3)

LARGE, forest cover consisting predominately of

large conifers. A fourth class for roads was also

included in the CLAMS study, but is not used for

our analysis. Data from Robison et al. (1999) were

used to estimate bias in density estimates arising from

the inability to see small landslides under tree canopy

in aerial photographs (Pyles and Froehlich, 1987;

Brardinoni, 2001) and to account for spatial variability

in topographic control on landslide susceptibility

(Miller et al., 2002).

Fig. 1. Landslide-inventory sites used for evaluating scale effects on landslide density. The SNF study (Bush et al., 1997) encompassed over

4000 km2 in two blocks, indicated by the green polygons on the map of western Oregon. The yellow polygons indicate the study sites included

in the ODF study (Robison et al., 1999). Landslide locations mapped in the SNF study are shown with white dots on the shaded relief images

to the right. Forest-cover types described in the text are indicated by color.


We found that the relative landslide density between

these three cover types varied as a function of scale.

For sample areas spanning tens of square kilometers,

there is a high probability that observed landslide

density is highest in the LARGE cover type (Fig. 2),

as observed by Robison et al. (1999). But at scales of

hundreds of square kilometers, observed densities are

almost always lowest in the LARGE cover type.

This dependence on sample scale arises in part

because the sample area is smaller than the character-

istic scale of heterogeneity in the spatial distribution of

landslides, a concept related to the representative

length in continuum mechanics (e.g. Middleton and

Wilcock, 1994) and the elementary unit volume in

fluid dynamics (Bear, 1972). We found that the range

of observed landslide densities varied as a function of

the area sampled (Fig. 3). A large range in densities is

found for small sample areas, with a large proportion

of the samples containing no landslides at all. Two

changes occur as the sample area increases: excluding

zero values, both the range and modal value of

observed landslide densities asymptotically decrease.

The decrease in modal value (Fig. 3) occurs because

about 20% of the samples—those with zero values,

primarily small sample areas—are excluded. Similar

biasing occurs with field studies, because site surveys

and resulting conclusions focus on areas that have

landslides. With all samples included, the modal value

remains constant with sample area. If the sample area

is small, there is a probability of observing a high

landslide density. If the area covered by one particular

cover type in a sample tends to be smaller than the

others, there is a probability of finding a higher land-

slide density in that cover type solely because of the

differences in area.

Excluding roads, the Bush et al. (1997) study area

included 21% in the OPEN class, 55% in the MIXED

class, and 24% in the LARGE class. Robison et al.’s

(1999) six sites included 17% in age classes less than

10 years, 61% in age classes from 10 to 100 years, and

22% in age classes exceeding 100 years. May’s (1998,

2002) sites included 23% in clearcut units, 47% in

second-growth stands, and 30% in mature forests. This

difference in area between cover types may account

for the behavior observed for the MIXED and LARGE

classes (Fig. 2), because most samples have a smaller

proportion of their area in the LARGE class. It does

not explain the relationship between the OPEN and

LARGE classes, however, since these two classes

involve similar areas. This suggests that the length

scale required to average variability in the LARGE

cover class is greater than for the MIXED class,

Fig. 2. The landslide inventory from the SNF study (Fig. 1) was subsampled over a range of scales. For any contiguous sample block

containing landslides in more than one cover type, the probability that landslide density in the ‘‘LARGE’’ cover type is greater than that in

either the ‘‘OPEN’’ or ‘‘MIXED’’ cover types varies as a function of the size of the sample block.


although other unexplored sampling issues may be

involved.

These results show that landslides are found in

dense clusters over tens of square kilometers with

large intervening areas containing few landslides.

They also suggest that landslides tend to be clustered

more tightly in old forests and more evenly distributed

in other forest types. Conclusions regarding the

influence of vegetation on landslide susceptibility

may thus vary dramatically depending on the scale

of observation. The large scale of heterogeneity that

must be accommodated complicates characterization

of landslides and other sediment-moving events.

The scale effects described above result from varia-

bility in the attributes being measured, which in this

case are landslide locations. Many factors create

variability in the production and delivery of sediment

to stream channels. Observed differences in the spatial

density of landslides are explained in part by varia-

tions in geology, topography, and vegetation (e.g.

Dragovich et al., 1993a,b). Such controls can be

quantified and, and to the extent and resolution that

they are mapped, their relative effect on landslide rate

can be anticipated, as is done for landslide-hazard

mapping (e.g. Hammond et al., 1992).

There are other factors whose influences on land-

slide location are unknown a priori. Spatial variability

in storm characteristics provides an example. The

storm in February 1996 that triggered the landslides

mapped in Oregon, although regionally extensive,

exhibited large variability in rainfall intensity (Oregan

State University, 1996; Taylor, 1997b, see also http://

www.ocs.orst.edu/gifs/flood_map.GIF). Convective

storms can also generate local high-intensity cells over

spatial scales of kilometers. Spatial variability in storm

intensity thus creates heterogeneity in sediment pro-

duction rates over scales spanning distances from one

to hundreds of kilometers.

The distribution of soil depths poses another

unquantified source of variability in factors controlling

sediment production (Dunne, 1998; Schmidt, 1999).

Soil depth is an essential factor in stability of hillslope

soils (Hall et al., 1994) and in setting the volume of

sediment available for delivery to a channel system

(Benda and Cundy, 1990). The spatial distribution of

soil depth over any area, coupled with the future

sequence of fires and storms, determines in part the

number of landslides that will occur within that area

over any specified period of time. If a series of storms

triggers a large number of landslides that evacuate the

soil from landslide-prone hollows, the distribution of

soil depths is changed along with the potential for

future landsliding. The spatial distribution of soil depth

and the potential for sediment delivery to the channel

system is thus a function of past events (Benda and

Dunne, 1997b). Given the time scales involved for

colluvial refilling of hollows (Dietrich and Dunne,

1978; Reneau et al., 1990), that history may span many

centuries. The past sequence of storms, fires, and other

vegetation disturbances, such as disease and wind-

throw, create a mosaic of soil properties with variability

over scales spanning meters to hundreds of kilometers.

Our recourse in dealing with effects of stochastic

and heterogeneous processes like storms and fires is to

Fig. 3. The upper graph is a scatter plot of landslide densities from

50,000 randomly placed sample blocks within the two SNF study

areas shown in Fig. 1. Densities are shown for the entire sample

block with no separation of cover type. The slanted arrays of

aligned dots correspond to samples containing one landslide (the

lowest, left-most array), two landslides, and so on. About 20% of

the samples had no landslides. The proportion of samples with no

landslides is shown as a function of sample size in the lower graph.


HTTP://WWW.OCS.ORST.EDU/GIFS/FLOOD_MAP.GIF

HTTP://WWW.OCS.ORST.EDU/GIFS/FLOOD_MAP.GIF

characterize them empirically in terms of probability

distributions. The use of probability distributions is

well established for estimating storm intensities and

peak flows for specific intervals of time. We can do the

same with patterns of spatial heterogeneity in sedi-

ment production arising from unquantified sources,

such as potential variations in soil depth. For example,

soil geotechnical properties are variable over scales

affecting individual landslides and gullies and prob-

abilistic descriptions of soil properties are used in

estimates of slope stability (Hammond et al., 1992).

2.1. Stochastic interactions: temporal–spatial

correlations

Stochastic erosional drivers acting over a heteroge-

neous topography create an erosion regime character-

ized by episodic patches of activity. The size and

location of these patches depends on the interactions

of fires, storms, and topography, which we illustrate

here with examples from central Idaho. The Boise

National Forest has experienced numerous large fires

over the last century (Fig. 4). During the last 12 years,

fire intensity, measured by crown scorch, was mapped

from the air for several of these fires. Over this time

period, landslides, gully erosion, and evidence of stream

disturbance were also mapped from 1:15,800-scale

aerial photographs (Fig. 5). Mapped patch sizes for

variations in fire intensity have length scales on the

order of 1–5 km. These fires had a decidedly non-uni-

form influence on patterns of mass wasting and asso-

ciated channel disturbance. The ‘‘patches’’ of stream

disturbance are individually larger than the patches of

high-intensity burn; stream disturbances may initiate

within high-intensity burn patches and then propagate

through lower-intensity burn and unburned areas.

Disturbed channels concentrated in patches with

length scales on the order of 5–10 km are also evident

(Fig. 5). These patches cluster in and near recent fires,

but several fall outside burned areas. Examination of

event timing reveals a mixture of causes. At large

(between group) scales, much variability is explained

by whether or not a severe weather event struck the

area. One particularly large thunderstorm in summer

1996 (prior to the aerial photography) affected several

streams just slightly north and west of the center of the

basin. The cluster in the southwestern part of the basin

was affected primarily by a thunderstorm in 1993,

shortly after the fire. Although not shown on this map,

the 1 January, 1997 rain-on-snow event affected

patches in the southwestern part of the basin again,

and several streams immediately north of the mapped

area in an area burned in 1989. The clustering in these

groups is similar to that seen in Fig. 5. All affected

streams were below 1500 m in elevation. Variations in

burn intensity explain only part of the controls on mass

wasting in individual basins in the area of that storm.

The debris flow on the far-eastern side of the basin

resulted from a small thunderstorm centered over one

flank of the basin. After the event, one could walk

across a hillslope with relatively uniform burn severity

and see the erosional response change from severely

eroded to undisturbed within 500 m although no var-

iation in fire severity (as measured by soil character-

istics) was observed over that transect. These

observations suggest that the scale of variability in

the driving weather exerts a strong control on the

spatial extent of subsequent erosion.

It is useful to compare the patch size of stream

disturbance seen in these examples to the size of

habitat patches used by fish (Fig. 6). Variations in

summer water temperature are the hypothesized

source of fragmentation for bull trout (Salvelinus

confluentus) in this basin, which yields elevation as

a control on the distribution of spawning and rearing

habitat (Dunham and Rieman, 1999). Dunham and

Rieman (1999) found that larger patches were more

likely to be occupied, in part because larger patches

yield larger, more diverse, more stable, and better-

connected populations of fish. Smaller patches are also

at risk of losing all of their habitat to mass wasting or

channel disturbance during a single event, whereas a

coherent set of disturbances over a patch the size of the

larger basins has not been seen in the last 15 years,

although fires of a size large enough to cover several

habitat patches are not unusual in the historical record.

If the spatial extent of stream disturbances are con-

trolled more by the intersection of fire and weather

than by the occurrence of fire alone, then fire alone is

unlikely to cause extirpation of more than one or a few

local populations during a given fire episode.

Interactions between climatic events and topogra-

phy also play an important role in setting the patch

scale over which erosional events are concentrated.

For example, the distribution of landslides mapped by

the Payette National Forest following a rain-on-snow


event in January 1997 revealed that elevation was

influential (Fig. 7). Most (94%) of the landslides were

between elevations of 1000 and 1500 m. Focusing

on this elevation range, 87% of these landslides

occurred on slopes steeper than 278 (estimated from

a DEM). Here we see a relatively uniform storm, a

large synoptic system with high spatial correlation in

precipitation, coming over complex topography to

form a distinct pattern in geomorphic response.

2.2. Controls on event occurrence

To quantify relationships of cause and effect on

the frequency and magnitude of stream disturbance

Fig. 4. Fires over 100 ha mapped since 1908 on the Boise National Forest. Some areas have burned up to five times during that period.


caused by sediment-moving events, it is useful to

define a conceptual model of the processes involved.

From the discussion above, and capitalizing on work

by Benda and Dunne (1997a,b; further described in

Benda et al., 1998), we identified three primary com-

ponents:

(1) A spatial template imposed by topography,

bedrock lithology, geologic structure, and soil

type that controls locations of sediment produc-

tion and storage and sets points of delivery to the

channel system.

(2) A set of stochastic temporal drivers that alter

erosional susceptibility and trigger sediment

fluxes, e.g. fires and storms.

(3) The antecedent sequence of events, which with

the rate of sediment production, determines the

volume of sediment available for delivery to and

transport through the channel system.

These three concepts provide a framework with

which to interpret and anticipate differences in dis-

turbance regimes, but to be useful in quantifying any

differences, we must develop quantitative character-

izations of each component and of interactions

between them. We describe strategies for charac-

terizations of topography, fire regime, and storm

climate in the following sections. Characterization

of the antecedent sequence of events, or at least of

their consequences, poses a considerable challenge.

Fig. 5. Middle Fork Boise River basin showing fires since 1989 and streams with evidence of major bed disturbance. Estimates of fire intensity

are based on extent of crown scorch and disturbed channels are mapped from aerial photographs.


For example, we have no means for efficient high-

resolution measurement of soil depths over watershed

scales. Likewise, the large temporal and spatial scales

involved hinder quantification of process interactions.

In the final section, we discuss use of numerical models

as a means of addressing these issues and as a tool for

exploring the role of different factors in controlling the

frequency and magnitude of sediment fluxes.

2.2.1. Topography

Topographic attributes represent large controls on

susceptibility to mass wasting (e.g. Dietrich et al., 2001)

and surface erosion (Dietrich et al., 1992). Topography

also determines where in the landscape colluvium will

accumulate (Hack and Goodlett, 1960; Dietrich and

Dunne, 1978) and dictates the points of delivery for

water-eroded and mass-wasting derived sediment to

the channel network (Swanson et al., 1988; Benda

and Dunne, 1997b). The advent of digital elevation

data and a variety of tools and algorithms for using

it (e.g. Zevenbergen and Thorne, 1987) make spa-

tially distributed estimates of topographic attributes

straightforward. Coupled with field observations of

erosional processes, topographic data can be used to

Fig. 6. Channels with major channel disturbance events since 1989 in the Middle Fork Boise River basin juxtaposed with bull trout habitat

patches (after Dunham and Rieman, 1999).


constrain the probability of erosional inputs to channel

systems (Istanbulluoglu et al., 2002).

We illustrate these concepts using an example for

debris flows in the Oregon Coast Range, based on

work done with Coastal Landscape and Analysis

Study (http://www.fsl.orst.edu/clams/). Although this

example deals with a particular mass-wasting process,

the techniques are applicable to any topographically

controlled erosional process.

It is convenient to separate topographic controls on

debris-flow occurrence between those that affect

initiation and those that affect the downslope scour,

transport, and deposition of material. Debris flows are

often initiated by shallow landsliding of colluvial

Fig. 7. Landslides following January 1997 rain-on-snow event within study areas in the Payette National Forest. Lighter shading indicates

areas between 1000 and 1700 m elevation.



material accumulated in topographic hollows (Dietrich

and Dunne, 1978). Stability of shallow colluvial

deposits can be estimated using a simple model—

the infinite slope approximation—with a topographic

dependence on slope gradient alone (e.g. Hammond

et al., 1992). Shallow landslides are triggered by

increased pore-pressure gradients during periods of

intense precipitation (Caine, 1980), which can be

estimated as a function of rainfall intensity, upslope

contributing area, and local slope (O’Laughlin, 1986).

These two models point to local surface gradient and

specific contributing area as primary topographic

controls on shallow landsliding (Montgomery and

Dietrich, 1994). Iverson (2000) highlights limitations

to the hydrologic assumptions used in this model, but

still recognizes the importance of local slope and

specific contributing area in setting the antecedent

soil moisture conditions that modulate the impact of

transient periods of high-intensity rainfall on slope

stability. We thus use a function of local slope and

specific contributing area (that of Montgomery and

Dietrich (1994), with soil parameters held uniform), as

a topographic index of slope stability. Using landslide

inventories, this index can then be calibrated as a

function of relative landslide density. This provides

a spatially distributed estimate of topographic control

on susceptibility to shallow landsliding and associated

debris-flow initiation.

Once initiated, subsequent downslope travel dis-

tance of a debris flow can be parameterized in terms of

several topographic attributes. Benda and Cundy

(1990) identified channel gradient and channel junc-

tion angles along the debris-flow track as dominant

controls. CLAMS (Miller et al., 2002) has expanded

on their work to include cumulative scour and de-

positional length as a proxy for debris-flow volume

(Iverson et al., 1998; May, 2002) in a probabilistic

model of debris-flow runout. This model was calibrated

using field mapping done by the Oregon Department of

Forestry (ODF) following the 1996 storms (Robison

et al., 1999) in the Oregon Coast Range.

Coupling probability estimates of landslide initia-

tion and debris-flow runout provides an estimate for

the probability of debris-flow delivery of material to a

channel (Fig. 8). For example, in the Siuslaw River

basin in coastal Oregon, topographic differences

between Knowles Creek basin, to the east, and Sweet

Creek basin, to the west, result in large differences in

the predicted probability of debris-flow delivery

between these two channel systems. Large variability

exists even within smaller sub-basins within each sys-

tem. We expect that such differences in the topographic

controls on debris-flow behavior between basins will

affect the frequency and magnitude of sediment deliv-

ery to the channel system, with consequences for the

frequency of habitat-altering disturbances within each

basin. Variations in the frequency and magnitude of

debris-flow events may also be manifest in current

distributions of channel and valley floor morphologic

attributes (Benda, 1990; Wohl and Pearthree, 1991) and

in the size of debris-flow fans (May, 2001), providing a

means for empirical verification of such hypotheses.

2.2.2. Fire

Myriad processes affect fire behavior, resulting in

complex patterns of fire occurrence over space and

time (Agee, 1993). Efforts to mechanistically model

fire behavior require large inputs of empirical data

(Keane et al., 1996), more perhaps than are feasible for

the large-scale (McKenzie et al., 1996) and long-term

models needed to characterize fire effects on erosion

and mass-wasting regimes. Simple characterizations

of fire occurrence covering basin to regional scales and

spanning centuries can be expressed in terms of the

mean rotation interval, a distribution of fire sizes, and

initiation frequency. Numerical models incorporating

stochastic aspects of fire size and ignition can then be

used to simulate fire sequences (Agee and Flewelling,

1983). From this basis, a variety of other controlling

factors can be included in long-term models. For exam-

ple, Benda and Dunne (1997b) included increased

ignition probability following fire, Wimberly (2002,

see also Wimberly et al., 2000) included variable burn

severity, and Benda et al. (1998; see also USDA Forest

Service, 2002) included topographic controls on fire

spread. The primary constraints for use of such models

are availability of data to characterize the controlling

factors.

Estimates of fire rotation can be made from den-

drochronology of fire scars (e.g. Agee et al., 1990) and

stand-age distributions (Van Wagner, 1978), both of

which depend on the age distribution at the time of

observation. Using a fire-simulation model, Wimberly

et al. (2000) showed that stand-age distributions

can vary dramatically over time with a range of

variation that is a function of the area observed


(see also Sprugel, 1991). Stratigraphic studies (Long

et al., 1998; Millspaugh et al., 2000; Mohr et al., 2000)

provide estimates over much longer time intervals and

show temporal variability in average fire recurrence

intervals over a range of scales (Whitlock et al., this

issue).

Estimates for the size distribution of fires come

from observed historical fires (e.g. Strouss et al., 1989)

and from dendroecological reconstructions of past

fires (Teensma, 1987; Impara, 1997). Such studies

indicate positively skewed size distributions charac-

terized by many small fires and few large ones. In

long-term fire-simulation models, Benda and Dunne

(1997b) characterized fire size using a negative expo-

nential distribution and Wimberly et al. (2000) used a

size distribution characterized by the inverse of the

mean size.

2.2.3. Storm climate

The storm events that trigger erosional processes

can also be characterized using probability distribu-

tions. Benda and Dunne (1997b; see also Lancaster

et al., 2000), e.g. used independent negative exponen-

tial distributions of storm frequency and duration,

based on work by Eagleson (1972). Miller (in USDA

Forest Service, 2002) used a multiparameter distribu-

tion that accounts for correlations between frequency

and duration.

These examples are calibrated to empirical rainfall

records and can be used to generate a sequence of

events that reproduce the stochastic nature of storms

over time, but which lack spatial variability. Hydrol-

ogists must deal with issues of spatial variability as

well, as shown by a long and prolific literature on the

subject of spatial scaling for design precipitation

Fig. 8. The probability of debris-flow impacts, including scour and deposition, based on topography for Knowles Creek and Sweet Creek

basins, Coast Range, Oregon. Topographic controls on debris-flow initiation and runout length are calibrated to debris-flow events mapped by

the ODF (Robison et al., 1999) during the storm of February 1996 discussed in the text.


events (e.g. US Weather Bureau, 1957; Rodriguez-

Iturbe and Mejia, 1974; Waymire et al., 1984;

Rodriguez-Iturbe, 1986; Sivapalan and Bloschl,

1998; Seed et al., 1999 are a small sample). One of

the primary tools used to describe this concept is the

areal reduction factor (ARF), which estimates the

fractional depth of point rainfall expected when con-

sidering a basin with some finite area. These curves are

used with intensity-duration-frequency curves derived

from statistics of individual precipitation gages to

design flow structures and retention basins for catch-

ments with some area. In general, they show that the

average precipitation of a large area is less than that of

a point. This is more pronounced for peaks with short

duration because such peaks are typically associated

with storms with small spatial extent. Besides simple

spatial variability in precipitation, variability in soil

water inputs caused by varying snowmelt with eleva-

tion during rain-on-snow events would also be a strong

control on spatial coherence in climatic drivers to

geomorphically significant events.

Conceptually, introducing ARFs into time series

modeling of hillslope and channel sediment fluxes

could be accomplished fairly directly using stochastic

climate modeling. Note that depth-duration-frequency

(DDF) curves essentially quantify the degree of con-

centration of rainfall in time, and one can view the

ARFs as quantifying the degree to which the rainfall is

concentrated in space. Parametric (e.g. Hanson et al.,

1994) or resampling-based (Rajagopalan and Lall,

1999) approaches have been used to generate point

rainfall depth-duration combinations, with somewhat

better results from resampling. Recognizing that the

ARFs essentially add another dimension to IDF

curves, one could conceptualize it as a separate IDF

chart for different areas, with the changes in the depth

for each duration between charts given by the ARF.

Depth, duration, and a randomly drawn frequency

would specify an area.

There are some minor theoretical shortcomings to

this approach that require attention. Many ARFs are

fixed-area ARFs, when really what is needed is a

storm-centered ARF. Storm-centered ARFs are gen-

erally only slightly smaller (Bloschl, 1996). In addi-

tion, very little care has been taken in understanding

the seasonality of ARFs and that the ARF may change

shape with return period (Bloschl, 1996). ARF curves

depend strongly on how precipitation in one location

is correlated with precipitation in another location.

During large synoptic storms, one expects coherence

over fairly large distances, e.g. several tens of kilo-

meters. During convective precipitation events corre-

lation may only exist on the scale of about 1 km

(Bloschl, 1996). The fact that there is seasonality to

the shape of ARF curves is important when discussing

impacts of fire in forested ecosystems. Fire-induced

water repellency occurring in some vegetation and

soil types may lead to the formation of gullies for

particular rainfall intensities (Istanbulluoglu et al.,

2002). Because higher rainfall intensities are typically

associated with convective storms, spatial temporal

modeling of geomorphology in areas where this is

important would need to consider the low spatial

correlation of rainfall.

One additional challenge in applying ARFs to this

modeling approach is that when there is no spatial

correlation in rainfall, different points within a catch-

ment are essentially operating independently. Thus for

a given area, we may potentially need to simulate

more than one storm. In the simple view adopted in

earlier modeling, where the entire model domain was

subjected to the same rainfall, complete correlation

is assumed. When loss of correlation is considered

(either from increased model domain or shorter cor-

relation lengths), we need to consider the possibility of

storm cells located in more than one part of the model

domain at a time. There is no simple approach for

this problem, and a range of spatio-temporal models

for precipitation simulation have arisen to solve it

(e.g. Waymire et al., 1984; Rodriguez-Iturbe, 1986;

Seed et al., 1999; Seed, 2001). Conceptually one could

also resample radar image sequences by expanding on

existing vector resampling methods (e.g. Rajagopalan

and Lall, 1999).

Note that the spatial scale problems outlined

here are a fundamental problem with simple risk

analyses applied for the US Forest Service’s Burned

Area Emergency Rehabilitation (BAER) program (see

http://www.fs.fed.us/biology/watershed/burnareas/)

which assumes uniformity of precipitation over a fire

regardless of fire size. For large fires, it is unlikely that

a storm will cover the whole fire, but somewhat likely

that somewhere within a large fire, severe conditions

will occur over a small area.

Potentially, we can consider effects of spatial varia-

bility in snowmelt with greater ease for areas where it


HTTP://WWW.FS.FED.US/BIOLOGY/WATERSHED/BURNAREAS/

is an important process in triggering large geomorphic

events. Variability in snowmelt during rain-on-snow

events appears at gross scales to be controlled by

elevation, essentially as a surrogate for temperature.

Below a given elevation, liquid precipitation com-

bined with positive sensible latent and sensible heat

to the snowpack can produce substantial soil water

inputs, whereas above that elevation precipitation falls

mostly as snow, and turbulent fluxes generally cool the

snowpack. By generating stochastic sequences that

maintain dependence structures between precipitation

and temperature (Rajagopalan and Lall, 1999), we can

estimate soil water input as a function of elevation

from a snowmelt model in areas where the process

might be important.

3. Modeling process interactions

3.1. Numerical models

As we have discussed, the factors that control

sediment fluxes exhibit variability over a range of

scales and quantification of these factors must accom-

modate variability over tens to hundreds of kilometers

and hundreds, perhaps thousands, of years. Interac-

tions that drive sediment inputs may be impossible

to discern using measured spatial and temporal

sequences at smaller scales (Kirchner et al., 2001),

yet knowledge of factors controlling their frequency

and magnitude, the spatial extent of affected stream

channels, and spatial synchrony between basins is

crucial to anticipating affects of land management

and climate change on aquatic ecosystems (Reeves

et al., 1995, Dunham et al., this issue).

To skirt the limitations imposed by observations

that span only a few decades, Benda and Dunne

(1997a,b) used numerical models to examine process

interactions over millennial time scales in a 200 km2

basin in western Oregon. They showed how super-

imposed storm and fire sequences, acting over hetero-

geneous topography, drive episodes of sediment

delivery to a channel system. Use of a numerical

model allowed them to generate event sequences over

time and space scales large enough to reveal formation

of distinct patterns in sediment transport and storage

through a channel network and to show how such

patterns emerge from the interaction of fires, storms,

topography, and channel-network geometry over an

entire basin. The existence and source of such patterns

must still be established through field studies, but their

prediction shows how process interactions over large

scales may be manifest and can guide field investiga-

tions to test these ideas.

Benda and Dunne (1997a,b) illustrated the use of a

‘‘top-down’’ or ‘‘hierarchical’’ modeling approach

(Murray, 2002), in which processes are described at

the scale of interest (Werner, 1999). In their case, that

scale was that of a channel reach—hundreds of

meters—over annual time steps. They generalized pro-

cesses of sediment flux and fluvial transport over these

scales. This strategy seeks process descriptions at scales

relevant to the system at hand, e.g. a river network, and

requires parameterizations that reduce degrees of free-

dom to those active at that scale. This is in contrast to a

reductionist strategy, which seeks to describe large-

scale systems from the ‘‘bottom-up’’, starting from the

underlying processes evident at smaller scales, e.g.

fluvial transport of sediment grains. Both approaches

add to our understanding of natural systems, but hier-

archical models are needed to explore interactions at

scales pertinent to the frequency, magnitude, spatial

extent, and synchrony of channel disturbance.

Hierarchical models have a variety of uses. They

provide a means of visualizing concepts over basin

scales. Benda et al. (1998) used model results to

illustrate effects of basin size and position in a channel

network on sediment yields and probability distribu-

tions of sediment storage in channel reaches. TheUSDA

Forest Service (2002) used model animations to show

how fires, storms, landsliding, and fluvial transport can

interact to produce variability in large woody debris

and sediment storage through a river network.

These models can be used to explore the conse-

quences of process interactions. Benda and Dunne

(1997a) predicted that the overlapping effects of fires

and storms drive episodic influxes of sediment to

channels that initiate pulses of sediment transport

through the network. In contrast, Lancaster et al.

(2000) predicted that effects of woody debris on

debris-flow runout distance cause low-order basins

to act as long-term sediment stores that gradually

meter sediment out to larger channels, thereby diffus-

ing the capacity for episodes of landsliding to generate

pulses of fluvial transport through the high-order net-

work. Differences in model predictions highlight the


potential role of specific factors and motivate field

measurements to test these hypotheses.

As experience with these types of models grows,

their utility will expand. They will be used as explora-

tory tools to evaluate the influence that differences in

topography or changes in climate or fire regime might

have on sediment fluxes and associated channel dis-

turbances. They will be used to evaluate the time

scales of response and recovery and the role of history

in setting channel and basin responses to storm and fire

events. Importantly, they will be used in scenario

testing to evaluate the likely consequences of different

management strategies (Dunne et al., 2001).

3.2. Data requirements

Two general types of information are required to

build numerical models: (1) data to characterize the

driving events, e.g. fires and storms, and (2) data to

characterize controls on consequent erosional events.

The models referenced here lack several important

factors: characterization of fire distributions from

stand-age mapping as used by Benda et al. (1998)

misses potentially important aspects of fire intensity;

use of spatially uniform storm events misses important

aspects of spatial variability in storm intensity; and

currently available digital elevation data cannot

resolve small-scale topographic controls on gully

initiation and landsliding. However, progress is being

made on all fronts. Aerial mapping of fire intensity

provides information on fire size distributions and

field mapping of associated effects (e.g. changes in

soil infiltration capacity) links fire intensity to con-

sequent impacts. Doppler radar may provide a means

of characterizing the spatial variability of rainfall

intensity associated with single storms and provide

information to estimate the size and frequency dis-

tribution of storm events. New methods for remotely

sensed elevation measurements, such as laser altime-

try (LIDAR), can provide high-resolution topographic

data. The next challenge may be to find the resources

to use available data.

Currently, basin-scale models can produce tempo-

rally and spatially distributed estimates of sediment

flux. Process-based models to translate estimates of

sediment flux and storage to temporal and spatial

predictions of biologically pertinent channel charac-

teristics, such as substrate texture (Dietrich et al., 1989;

Buffington and Montgomery, 1999; Lisle et al., 2000)

or pool extent (USDA Forest Service, 2002) must still

be incorporated. Data to characterize the consequences

to channels of changes in sediment volume and to

characterize biological responses to those changes are

essential for using numerical models to interpret and

infer the consequences of past and future changes in

fire regime, climate, and land management.

4. Conclusions

Sediment fluxes and consequent stream-channel

disturbances are driven by process interactions over

time periods spanning centuries and spatial scales

spanning entire river basins. Methods for data collec-

tion and analyses over these scales are being actively

developed, spurred by the realization that land-man-

agement practices, coupled with changes in climate,

can dramatically influence rates of sediment delivery

to stream channels. Stratographic and sedimentologi-

cal studies (e.g. Meyer and Pierce, this issue) are

greatly expanding records of past sediment-flux events

and point to strong climatic controls and large varia-

tions across regions. To anticipate the consequences of

land management, fire suppression, and climate

change, we require quantitative characterizations of

the processes that drive sediment fluxes and of the

factors that control the spatial and temporal patterns of

sediment delivery to stream channels. The stochastic

and heterogeneous nature of these processes leads us

to probabilistic descriptions and to development of

analytical methods that use probabilistic parameter-

izations. Predictive tools must also deal with the

effects of past events. These requirements have lead

to development of numerical models that can simulate

process interactions over large temporal and spatial

scales. As experience with these types of models

accumulates, they have the potential to provide a

useful analysis tool, offering a spatial and temporal

context for interpretation of field observations and

predictions that can be tested with field measurements.

Acknowledgements

The landslide density and topographic control on

debris-flow probability analyses reported on here were


done with support and assistance from the Coastal

Landscape Analysis and Modeling study through the

US Forest Service, Pacific Northwest Research Sta-

tion, Forest Sciences Laboratory, in Corvallis, Oregon.

Jim Paul and Jason Hinkle with the Oregon Depart-

ment of Forestry were also very helpful in providing

data from the 1996 storm study. We thank Christine

May, who provided data from her thesis work and

prompted many helpful discussions. Thanks to Kelly

Christiansen and Dave Nagel for assisting with

graphics production and to Jack King for aerial photo-

graph interpretation and mapping. We greatly appreci-

ate reviews by David Tarboton, John Buffington, and

an anonymous reviewer, which served to improve an

earlier version of this paper.

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